Linear-quadratic optimal control for abstract differential-algebraic equations
arxiv(2024)
摘要
In this paper, we extend classical approach to linear quadratic (LQ) optimal
control via Popov operators to abstract linear differential-algebraic equations
in Hilbert spaces. To ensure existence of solutions, we assume that the
underlying differential-algebraic equation has index one in the
pseudo-resolvent sense. This leads to the existence of a degenerate semigroup
that can be used to define a Popov operator for our system. It is shown that
under a suitable coercivity assumption for the Popov operator the optimal costs
can be described by a bounded Riccati operator and that the optimal control
input is of feedback form. Furthermore, we characterize exponential stability
of abstract differential-algebraic equations which is required to solve the
infinite horizon LQ problem.
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